Fundamentals of Momentum, Heat, and Mass Transfer
Fundamentals of Momentum, Heat, and Mass Transfer
6th Edition
ISBN: 9781118947463
Author: James Welty, Gregory L. Rorrer, David G. Foster
Publisher: WILEY
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Chapter 6, Problem 6.5P
Interpretation Introduction

Interpretation: The gage pressure for the given power of the turbine is to be determined by using the energy balance equation.

Concept introduction: The Energy balance across the pipe is given by the Bernoulli’s equation in which the sum of Potential head, Kinetic head and Pressure head is constant. The Bernoulli equation across 2 points of any system is given by:-

  P1ρg+v122g+ Z1+H=P2ρg+v222g+ Z2+hf ……. (1)

The notations used in equation (1) are:-

P1and P2are pressure at inlet and outlet of the pipe

v1 and v2 are velocity at inlet and outlet of the pipe

Z1 and Z2 are the locations of the liquid.

  ρ = Density of the water

H = Head developed by the pump

g = Acceleration due to gravity

hf = Frictional losses

The power delivered by the pump is given as for a given efficiency is,

   P =ηρgHQ ……. (2)

Q = Flow rate of the water

   P = Power of the pump

  η = Turbine efficiency

The flow rate is given as,

  Q=A×v ……. (3)

A = Area of pipe

v = Velocity of water

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